Predictions of supersymmetric grand unified theories

Renormalization effects are analyzed for a class of supersymmetric grand unified theories which contain the standard $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_c\times \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ model. Predictions for ${{sin}^2\hat{\theta }}_W\left(m_W\right)$ and the proton lifetime are obtained as functions of ${\Lambda }_{\overline{\mathrm{MS}}}$ ($\overline{\mathrm{MS}}$ is the modified minimal-subtraction scheme), $N_H$ (number of relatively light Higgs doublets), and $\mu$ (the scale of supersymmetry breaking). For realistic input parameters we find $0.23<~{sin}^2{\hat{\theta }}_W\left(m_W\right)<~0.26$ and ${10}^{38}\gtrsim {\tau }_p\gtrsim {10}^{29}$ yr. Loop effects that could render the larger predicted values of ${{sin}^2\hat{\theta }}_W\left(m_W\right)$ consistent with experiment are described.